SOLUTION: A school is planning to make toys and souvenirs to sell at the festival as a fundraiser. The students are divided into two groups - one group can make toys, the other group to make

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A school is planning to make toys and souvenirs to sell at the festival as a fundraiser. The students are divided into two groups - one group can make toys, the other group to make      Log On


   

Question 1146818: A school is planning to make toys and souvenirs to sell at the festival as a fundraiser. The students are divided into two groups - one group can make toys, the other group to make souvenirs.Because of time constraints due to classes, only 150 toys and 120 souvenirs can be made each week. Enough material is delivered to the school to make a total of 200 items per week. Each toy sold makes a profit of $2 and each souvenir sold makes a profit of $5. In order to make the most money from the fundraiser, how many of each item should be made each week?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your objective function is:
profit = 2x + 5y

your constraint functions are:
x <= 150
y <= 120
x + y <= 200
x >= 0
y >= 0

using the desmos.com calculator, i graph the OPPOSITE of the inequalities.
the area of the graph that is NOT shaded is my region of feasibility.
the corner points of this region are where the maximum / minimum values of the objective function lie.

the calculator i used can be found at https://www.desmos.com/calculator

here's my graph.

$$$

the largest profit is found when x = 80 and y = 120.
that's the point (80,120).
the profit at that point is 80 * 2 + 120 * 5 = 160 + 600 = 760.
all the constraints are met since.....
x <= 150
y <= 120
x + y <= 200
x >= 0
y >= 0